Algebra of generalized Hukuhara differentiable interval-valued functions: review and new properties

Abstract This article deals with the algebra of gH-differentiable interval-valued functions. Specifically, we give conditions for the gH-differentiability of the sum and the gH-difference of two gH-differentiable interval-valued functions; we also consider the product and the composition of a differentiable real function and a gH-differentiable interval-valued function. We briefly review existing results on the topic and show that some of them are not correct. New properties are also presented. Therefore, this article corrects, complements and generalizes previously obtained results. Some examples and counterexamples illustrate the theory.

[1]  Yurilev Chalco-Cano,et al.  Calculus for interval-valued functions using generalized Hukuhara derivative and applications , 2013, Fuzzy Sets Syst..

[2]  T. Allahviranloo,et al.  Note on ''Generalized Hukuhara differentiability of interval-valued functions and interval differential equations'' , 2012 .

[3]  Marek T. Malinowski,et al.  Interval Cauchy problem with a second type Hukuhara derivative , 2012, Inf. Sci..

[4]  Yurilev Chalco-Cano,et al.  Optimality conditions for generalized differentiable interval-valued functions , 2015, Inf. Sci..

[5]  Yurilev Chalco-Cano,et al.  Characterizations of generalized differentiable fuzzy functions , 2016, Fuzzy Sets Syst..

[6]  Tofigh Allahviranloo,et al.  SOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS , 2018 .

[7]  Luciano Stefanini,et al.  A generalization of Hukuhara difference and division for interval and fuzzy arithmetic , 2010, Fuzzy Sets Syst..

[8]  Ngo Van Hoa.  Existence results for extremal solutions of interval fractional functional integro-differential equations , 2018, Fuzzy Sets Syst..

[9]  Juan Tao,et al.  Properties of interval-valued function space under the gH-difference and their application to semi-linear interval differential equations , 2016, Advances in Difference Equations.

[10]  Tofigh Allahviranloo,et al.  On the fuzzy Poisson equation , 2018, Fuzzy Sets Syst..

[11]  Tofigh Allahviranloo,et al.  A fuzzy solution of heat equation under generalized Hukuhara differentiability by fuzzy Fourier transform , 2017, Fuzzy Sets Syst..

[12]  Yurilev Chalco-Cano,et al.  New efficiency conditions for multiobjective interval-valued programming problems , 2017, Inf. Sci..

[13]  Yurilev Chalco-Cano,et al.  Generalized derivative and π-derivative for set-valued functions , 2011, Inf. Sci..

[14]  Barnabás Bede,et al.  Generalized differentiability of fuzzy-valued functions , 2013, Fuzzy Sets Syst..

[15]  Tofigh Allahviranloo,et al.  On fuzzy solutions for heat equation based on generalized Hukuhara differentiability , 2015, Fuzzy Sets Syst..

[16]  Luciano Stefanini,et al.  Some notes on generalized Hukuhara differentiability of interval-valued functions and interval differential equations , 2012 .

[17]  Svetoslav Markov,et al.  Calculus for interval functions of a real variable , 1979, Computing.

[18]  Donal O'Regan,et al.  Solving interval-valued fractional initial value problems under Caputo gH-fractional differentiability , 2017, Fuzzy Sets Syst..